Let U be a weakly closed nest algebra module acting on a Hilbert space H. Given two operators X and Y in B(H), a necessary and sufficient condition for the existence of an operator T in U satisfying TX = Y is provided.
This article is devoted to the study of the symmetry in the Yetter-Drinfeld category of a finite-dimensional weak Hopf algebra.It generalizes the corresponding results in Hopf algebras.
We give the Fundamental Theorem for Hopf modules in the category of Yetter-Drinfeld modules , where L is a quasitriangular weak Hopf algebra with a bijective antipode. We also show that H* has a right H-Hopf mod...We give the Fundamental Theorem for Hopf modules in the category of Yetter-Drinfeld modules , where L is a quasitriangular weak Hopf algebra with a bijective antipode. We also show that H* has a right H-Hopf module structure in the Yetter-Drinfeld category. As an application we deduce the existence and uniqueness of right integral from it.展开更多
The duality theorem of generalized weak smash coproducts of weak module coalgebras and comodule coalgebras over quantum groupoids is studied.Let H be a weak Hopf algebra,C a left weak H-comodule coalgebra and D a left...The duality theorem of generalized weak smash coproducts of weak module coalgebras and comodule coalgebras over quantum groupoids is studied.Let H be a weak Hopf algebra,C a left weak H-comodule coalgebra and D a left weak H-module coalgebra.First,a weak generalized smash coproduct C×lH D over quantum groupoids is defined and the module and comodule structures on it are constructed.The weak generalized right smash coproduct C×rL D is similar.Then some isomorph-isms between them are obtained.Secondly,by introducing some concepts of a weak convolution invertible element,a weak co-inner coaction and a strongly relative co-inner coaction,a sufficient condition for C×rH D to be isomorphic to Cv D is obtained,where v∈WC（C,H）and the coaction of H on D is right strongly relative co-inner.Finally,the duality theorem for a generalized smash coproduct over quantum groupoids,（C×lH H）×lH H≌Cv（H×lH H）,is obtained.展开更多
Let H be a finite dimensional Hopf algebra and A a commutative H-module algebra. We prove that the smash product A#H is of the same weak global homological dimension as A, provided that H^＊ is unimodular and there is...Let H be a finite dimensional Hopf algebra and A a commutative H-module algebra. We prove that the smash product A#H is of the same weak global homological dimension as A, provided that H^＊ is unimodular and there is a trace one element in A.展开更多
文摘Let U be a weakly closed nest algebra module acting on a Hilbert space H. Given two operators X and Y in B(H), a necessary and sufficient condition for the existence of an operator T in U satisfying TX = Y is provided.
基金the National Natural Science Foundation of China(10301033 and 10271113)
文摘This article is devoted to the study of the symmetry in the Yetter-Drinfeld category of a finite-dimensional weak Hopf algebra.It generalizes the corresponding results in Hopf algebras.
文摘We give the Fundamental Theorem for Hopf modules in the category of Yetter-Drinfeld modules , where L is a quasitriangular weak Hopf algebra with a bijective antipode. We also show that H* has a right H-Hopf module structure in the Yetter-Drinfeld category. As an application we deduce the existence and uniqueness of right integral from it.
基金The National Natural Science Foundation of China(No.10871042)the Natural Science Foundation of Jiangsu Province(No.BK2009258)
文摘The duality theorem of generalized weak smash coproducts of weak module coalgebras and comodule coalgebras over quantum groupoids is studied.Let H be a weak Hopf algebra,C a left weak H-comodule coalgebra and D a left weak H-module coalgebra.First,a weak generalized smash coproduct C×lH D over quantum groupoids is defined and the module and comodule structures on it are constructed.The weak generalized right smash coproduct C×rL D is similar.Then some isomorph-isms between them are obtained.Secondly,by introducing some concepts of a weak convolution invertible element,a weak co-inner coaction and a strongly relative co-inner coaction,a sufficient condition for C×rH D to be isomorphic to Cv D is obtained,where v∈WC（C,H）and the coaction of H on D is right strongly relative co-inner.Finally,the duality theorem for a generalized smash coproduct over quantum groupoids,（C×lH H）×lH H≌Cv（H×lH H）,is obtained.
基金the National Natural Science Foundation of China (10271081) the Natural Science Foundation of Beijing (1042004)
文摘Let H be a finite dimensional Hopf algebra and A a commutative H-module algebra. We prove that the smash product A#H is of the same weak global homological dimension as A, provided that H^＊ is unimodular and there is a trace one element in A.
